Question

From a light house the angles of depression of two ships on opposite sides of the light house are observed to be 30° and 45°. If the height of the light house is h metres, the distance between the ships is
A. (√3+1)hmetres
B. (√3-1)hmetres
C. √3hmetres
D.1+(1+1/√3)hmetres

Answer 1

If the height of the light house is h metres, the distance between the ships is  (√3+1)h metres

Option A is correct.

In Δ AQB,

tan ∅ = AP / QB

tan 30° = h/y

1/√3 = h/y

∴ y = √3h ...........(1)

In Δ APB,

tan ∅ = AB / PB

tan 45° = h/x

1 = h/x

∴ x = h ...........(2)

Adding (1) and (2), we get,

x + y = h + √3h

From figure, we have,

PB + BQ  = h + √3h

PQ = (1+√3)h meters